From how far away could Earth be detected using our present technology? How many stars within that distance?
Thanks
JPL has a nice site on extra-solar plants, and a cool Shockwave atlas.
RA isn't here, so I'll attempt an answer. We've discovered about 150 extra-solar planets, some as far as 500 light years away. I don't know the number of stars in a sphere with that radius, but within a radius of only 250 light years there are 260,000 stars, according to this source: The Universe within 250 Light Years.
It's not clear if you mean using SETI technology, or using ANY technolgy. If the latter, PH has already provided you with an answer. If the former, which is in effect the same as asking how far away can we or a similar civilization of similar technology detect the sorts of radio signals that are generated on earth by humans, the answer is somewhere beyond 1000 LY, and substantially more if you use something the size of the Arecibo dish for your antenna. And even more than that again if Alfred the Alien is using an Arecibo size antenna to transmit his signals!
I'm quoting RA for the 1000 LY number, so if it turns out wrong, blame him!
Consider a sphere with a radius of about 80 light years. That would place many thousands of stars in such a sphere. We've been broadcasting for quite a while.